Consider two interconnected tanks, labeled A and B. Salt water with a concentration of 1 lb/gal is pumped into Tank A at a rate of 3 gal/min while Tank B is drained at the same rate. The contents of Tank A flow into Tank B at a rate of 4 gal/min and the contents of Tank B flow into Tank A at a rate of 1 gal/min. Initially, Tank A contains 2 lbs of salt dissolved into 10 gallons of water. Tank B initially contains 10 gallons of fresh water. Draw and label a diagram that represents the elements in this problem. Then set up differential equations that describe the amount of salt (in lbs) in each of the two tanks.

Consider two interconnected tanks, labeled A and B. Salt water with a concentration of 1 lb/gal is pumped into Tank A at a rate of 3 gal/min while Tank B is drained at the same rate. The contents of Tank A flow into Tank B at a rate of 4 gal/min and the contents of Tank B flow into Tank A at a rate of 1 gal/min. Initially, Tank A contains 2 lbs of salt dissolved into 10 gallons of water. Tank B initially contains 10 gallons of fresh water. Draw and label a diagram that represents the elements in this problem. Then set up differential equations that describe the amount of salt (in lbs) in each of the two tanks.

Name: Please help with the attached problem 10. Consider two interconnected
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please help with the attached problem 10. Consider two interconnected tanks, labeled A and B. Salt water with a concentration of 1 lb/gal is pumpedinto Tank A at a rate of 3 gal/min while Tank B is drained at the same rate. The contents of Tank A flo

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 15EQ

See similar textbooks

Similar questions

Two connected tanks, each with a capacity of 50 liters, contain brine (saltwater). Initially, the first tank contains 18 liters of brine with a salt concentration of 3 grams per liter and the second contains 17 liters of brine with a salt concentration of 2 grams per liter. At t = 0 brine with a salt concentration of 6 grams per liter flows into the first tank at 8 liters per hour. Well-stirred brine flows from the first tank into the second at 7 liters per hour, from the second into the first at 5 liters per hour, from the first into a drain at 4 liters per hour, and from the second into a drain at 3 liters per hour. (a) Determine the volume (liters) of brine in each tank as a function of time.(b) Give an initial-value problem that governs the amount (grams) of salt in eachtank as a function of time.(c) Give the interval of definition for the solution of this initial-value problem.
Suppose Tank A has 30 gallons of water containing 55 oz (ounces) of dissolved salt, Tank B has 20 gallons of water containing 26 oz of dissolved salt and Tank C has 50 gallons of water without any salt. Water with salt concentration 1 oz/gal flows into Tank A at a rate of 1.5 gal/min. Water flows in and out of tank A, B and C are as follows: Water with salt concentration 1 oz/gal flows into Tank A at a rate of 1.5 gal/min.Water flows from Tank A to Tank B at a rate of 3 gal/min.Water flows from Tank B to Tank A at a rate of 1.5 gal/min.Water flows from Tank B to Tank C at a rate of 3.5 gal/min.Water flows from Tank C to Tank B at a rate of 1 gal/min.Water drains from Tank C at a rate of 1.5 gal/min. a) Sketch the diagram that describe the above system. b) Determine the concentration of the brine inside each tank. c) Write the mathematical model that describe the above system.
Consider the two-tank connection pictured below. The salt water flows at specified rates and thesolution is assumed to be “well-stirred”. Each tank has a capacity of 5000 gal. Initially, Tank 1 has 500 gal. of fresh water and Tank 2 has 800 gal. of salt water with 2 lb of salt dissolved in it. Salt water with a concentration of 1/5 lb/gal enters Tank 1 at a rate of 4 gal/min and the mixture leaves at a rate of 7 gal/min at the same time. Salt water with a concentration of 1/4 lb/gal enters Tank 2 at a rate of 10 gal/min and the mixture leaves at a rate of 9 gal/min at the same time. Additionally, the mixture from Tank 1 flows into Tank 2 at a rate of 3 gal/min andthe mixture from Tank 2 flows into Tank 1 at a rate of 8 gal/min. Let Q1(t) and Q2(t) denote theamounts of salt in pounds in Tanks 1 and 2 at time t in minutes. Set up the initial value problemsfor Q1(t) and Q2(t) at time t. (Do not solve.)
solve and draw a diagram of the problem Two large tanks, each holding 100L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of 3L/min and from tank B into tank A at a rate of 1L/min. The liquid inside each tank is kept well stirred. Pure water flows into tank A at a rate of 6L/min. The solution flows out of the system from tank A at 4L/min and from tank B at 2L/min. If, initially, tank A contains pure water and tank B contains 20kg of salt, determine the mass of salt in each tank at time t ≥ 0.
Parent W requires one of component B and two of component C. Both B and Care run on work center 10. Setup time for B is 2 hours, and run time is 0.1 hour perpiece. For component C, setup time is 2 hours, and run time is 0.15 hour per piece. Ifthe rated capacity of the work center is 80 hours, how many Ws should be producedin a week?
Imagine that a manufacturing needs to produce 240 products weekly. The company has three manufacturing processes A, B and C. Machine A can finalize a product in 24 minutes; machine B 36 minutes and assembly line C can finalize in 12 minutes. How many machine A, B and C should the company invest to minimize Muda? Design its flow! 8 work hours per day
A plant food is made from three chemicals, labeled I, II, and III. In each batch of the plant food, the amounts of chemicals II and III must be in the ratio of 5to 3. The amount of nitrogen must be at least 39 kg. The percent of nitrogen in the three chemicals is 8%,4%,and 5%,respectively. If the three chemicals cost $1.02 $0.86 and $0.66 per kilogram, respectively, how much of each should be used to minimize the cost of producing at least 600 kg of the plant food?
An oil refinery is located 1 km north of the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 6 km east of the refinery. The cost of laying pipe is $400,000/km over land to a point P on the north bank and $800,000/km under the river to the tanks. To minimize the cost of the pipeline, how far downriver from the refinery should the point P be located? (Round your answer to two decimal places.)
A chemist makes a component of orchid fertilizer that requires two secret ingredients labeled as A and B. She sells ingredient A at Php 200 per kilogram and ingredient B at Php 350 per kilogram. Per production, a kilogram of ingredient A requires 4 units of special pollen while 3 units for each kilogram of ingredient B. Suppose the excess of ingredient B over ingredient A per production should be at most 4 units, and there are only 24 units of special pollen available per production, how many kilograms of ingredient A and ingredient B should be made per production to maximize the sales?
A cooperative society of farmers has 50 hectares of land for two crops, X and Y. Earnings for crops X and Y per hectare are estimated at Rs 10,500 and Rs 9,000, respectively. To control weeds, a liquid herbicide should be used for crops X and Y at a rate of 20 liters and 10 liters per hectare. Also, to protect fish and wildlife no more than 800 liters of herbicide should be used and a pond that collects drainage from this land is recommended. Use the principles of linear programming to determine how much land should be allocated to each crop in order to maximize the total benefit to society.